Decorative Threads that I use in art quilts are sorted as follows: Vintage and antique cotton thread is kept together in three vintage thread boxes sorted by color. Vintage cotton wrapped poly and nylon are kept in another set of vintage thread boxes also sorted by color. Vintage and modern silk, rayon and trilobal poly and metallics have their own boxes and Various specialty threads are in a couple of other boxes sorted by material and whether they are able to go through a needle or must be used for bobbin work or handwork only (think Razzledazzle and other lumpy shiny threads).
Thread that I'm certain is strong enough for everyday using quilts is stored in another box that includes thread for piecing as well as quilting--- these are strong modern threads such as aurifil, isacord, wonderfil, and some of superior's threads. I keep a limited range of colors in these threads so they are all stored together in one tin.
If there is thread left over on the bobbin when I'm done then the bobbin gets stored with the thread spool- depending on spool type and what kind of storage box I'm using they either get put in the little bobbin cubbies in the vintage thread boxes, or attached to the spool/ cone with Hugo's amazing tape.
Rob